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Question -

Three coins are tossed. Describe
(i) two events A and B which are mutually exclusive.
(ii) three events A, B and C which are mutually exclusive and exhaustive.
(iii) two events A and B which are not mutually exclusive.
(iv) two events A and B which are mutually exclusive but not exhaustive.



Answer -

Given: Three coins aretossed.

When three coins aretossed, then the sample space is

S = {HHH, HHT, HTH,HTT, THH, THT, TTH, TTT}

Now, the subparts are:

(i) The two eventswhich are mutually exclusive are when,

A: getting no tails

B: getting no heads

Then, A = {HHH} and B= {TTT}

So, the intersectionof this set will be null. Or, the sets are disjoint.

(ii) Three eventswhich are mutually exclusive and exhaustive are:

A: getting no heads

B: getting exactly onehead

C: getting at leasttwo head

So, A = {TTT} B ={TTH, THT, HTT} and C = {HHH, HHT, HTH, THH}

Since, A B = B C = C A = Փ and

A B C = S

(iii) The two eventsthat are not mutually exclusive are:

A: getting three heads

B: getting at least 2heads

So, A = {HHH} B ={HHH, HHT, HTH, THH}

Hence, A B = {HHH} = Փ

(iv) The two eventswhich are mutually exclusive but not exhaustive are:

A: getting exactly onehead

B: getting exactly onetail

So, A = {HTT, THT,TTH} and B = {HHT, HTH, THH}

It is because A B = Փ but A B ≠ S

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